Heat conduction equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg32848] Heat conduction equation*From*: "Maurizio Tomasi" <zio_tom78 at hotmail.com>*Date*: Fri, 15 Feb 2002 02:49:50 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello to everybody. I am trying to find a solution to the heat conduction equation (in one dimension) by using the Fourier transform. The equation has the following form: 2 d T d T C ------ + q delta(x) - k rho ----- = 0 2 d t d x and the Cauchy condition is / | i omega t T (x=x1, t=0) = | c (omega) e d omega | / (at some point x1 the temperature must have a pre-defined spectral shape). The Dirac delta in the equation represents a source of heat placed at x=0. Could somebody give me a reference or an hint about possible analytical solutions of this equation (in terms of generalized functions)? I managed to solve it by ignoring the second or the third term, but now I need a *general* solution. Thanks in advance Maurizio -- Posted via Mailgate.ORG Server - http://www.Mailgate.ORG